Abstract
In the present paper, under the continuum hypothesis, we construct an example of a discretely generated compact set X whose square is not discretely generated. For each compact set X, there is an ordinally valued characteristic idc(X), which is the least number of iterations of the d-closure generating, as a result, the closure of any original subset X. We prove that if χ(X) ≤ ω α , then idc(X) ≤ α + 1.
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Original Russian Text © A. V. Ivanov, E. V. Osipov, 2010, published in Matematicheskie Zametki, 2010, Vol. 87, No. 3, pp. 396–401.
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Ivanov, A.V., Osipov, E.V. Degree of discrete generation of compact sets. Math Notes 87, 367–371 (2010). https://doi.org/10.1134/S0001434610030077
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DOI: https://doi.org/10.1134/S0001434610030077